A Counterexample for Commutation in Tensor Products of C ∗ -Algebras

1981 ◽  
Vol 81 (4) ◽  
pp. 562
Author(s):  
R. J. Archbold
Keyword(s):  
Tensor Products ◽  
C Algebras

Operational independence and tensor products of C*-algebras

2017 ◽  
Vol 58 (3) ◽  
pp. 032303
Author(s):  
Jan Hamhalter ◽  
Shuilin Jin
Keyword(s):  
Tensor Products ◽  
C Algebras

A Commutation Result for Tensor Products of C * -Algebras

1973 ◽  
Vol 5 (3) ◽  
pp. 283-287 ◽  
Author(s):  
Richard Haydon ◽  
Simon Wassermann
Keyword(s):  
Tensor Products ◽  
C Algebras

scholarly journals P-Tensor Product for Group C*-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 627
Author(s):  
Yufang Li ◽  
Zhe Dong
Keyword(s):  
Tensor Product ◽  
Free Group ◽  
Discrete Group ◽  
Tensor Products ◽  
Haagerup Property ◽  
C Algebras ◽  
P Tensor

In this paper, we introduce new tensor products ⊗ p ( 1 ≤ p ≤ + ∞ ) on C ℓ p * ( Γ ) ⊗ C ℓ p * ( Γ ) and ⊗ c 0 on C c 0 * ( Γ ) ⊗ C c 0 * ( Γ ) for any discrete group Γ . We obtain that for 1 ≤ p < + ∞ C ℓ p * ( Γ ) ⊗ m a x C ℓ p * ( Γ ) = C ℓ p * ( Γ ) ⊗ p C ℓ p * ( Γ ) if and only if Γ is amenable; C c 0 * ( Γ ) ⊗ m a x C c 0 * ( Γ ) = C c 0 * ( Γ ) ⊗ c 0 C c 0 * ( Γ ) if and only if Γ has Haagerup property. In particular, for the free group with two generators F 2 we show that C ℓ p * ( F 2 ) ⊗ p C ℓ p * ( F 2 ) ≇ C ℓ q * ( F 2 ) ⊗ q C ℓ q * ( F 2 ) for 2 ≤ q < p ≤ + ∞ .

Finite Lattices of Projections in Factors and Approximately Finite C*-Algebras

1992 ◽  
Vol 35 (1) ◽  
pp. 116-125
Author(s):  
S. C. Power
Keyword(s):  
Tensor Product ◽  
General Result ◽  
Finite Lattice ◽  
Tensor Products ◽  
C Algebras ◽  
Finite Lattices

AbstractA unique factorisation theorem is obtained for tensor products of finite lattices of commuting projections in a factor. This leads to unique tensor product factorisations for reflexive subalgebras of the hyperfinite II1 factor which have irreducible finite commutative invariant projection lattices. It is shown that the finite refinement property fails for simple approximately finite C*-algebras, and this implies that there is no analogous general result for finite lattice subalgebras in this context.

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